Vladimir

I think Vlad is the biggest counter of Zed. If you don't beat him in early you are done later. He is weak in early game. (cooldowns and no escape)
But when he has cooldown items he starts be dangerous for you. Every trade with you is his win. because he will get hp back, you not (if not lifesteal).
Rush Executioner in early for reduce his heals. If you failed vs him in early. Try to rush hexdrinker with Mercury boots. Vladimir's weakness are ignite and Grevious wound (mortal reminder and morello)

Fizz

Good Fizz player can outplay you easy. Fizz main will hit you with ult and wait with his W for your R dodge. So he will use W at same moment when you will want use R for dodge (shark). Always watch his W and don't waste your W for poking him to much. You will need it for escape or make outplay. Good item vs Fizz will be new Edge of night. Shield will protect you from his ultimate.

Lissandra

Lissandra is big counter of Zed, Dangerous for Zed is her R, which can save her from Zed's Death Mark (R).

Lissandra has 2 options for her ultimate.
1st use ultimate on you
2nd use ultimate on herself
Logical she will use her ult on you just when her jungler come.
And on herself when your jungler comes.

Good tip for you. Rush Qucksivle slash early or change ingite for cleanse in champ select. You can remove her W or ult from you.
If she will see you have one of them. She will always ult herself. And now it's your turn.
Always bait her with Death Mark (R). But don't use another spells. Wait until her ult will end and after use your spells and damage.Never waste your W before her E. Always save it for follow her or escape from her.

Kayle

Kayle counters you with her ultiamte (R). So always try to poke her to low hp before you will use your ultimate on her. If you have problem play vs Kayle. Take exhaust (no ingite) you will reduce her dmg and she wont escape from you. After her 16lvl don't try to fight with her 1v1 without W or flash. Items vs her? Executioner->Mortal reminder and Guardian Angel to late game

Swain

Swain is tanky mage which has lot of CC. Don't waste your W for poking him. Because he will root you with E and will take HP back with W. Executioner is good choice here too. When he is in ultimate and has 70%hp+ don't figt with him. Always wait until his ultimate will end. After he is killable.

Mordekaiser

Mordekasier after rework is one of the hardest enemies for Zed. He has high damage and his W (shield) is obstacle for Zed. Rush Quicksilver slash in early vs his ultimate. And Executioner with ingite will help you too vs his healing from W. Don't trade with im to much on melee range. Always poke him with Q over minions, when you are under your turret. You cna use WEQ combo too.

Diana

Akali

Ekko

Katarina

Not hard matchup. It's 50/50. Better player wins. Tip vs Katarina? Save your W for escape from her R. Same if you see she used QEW combo. You can go in.

LeBlanc

You can dodge her QWE AA combo with your WEQW combo.

Annie

Irelia

Qiyana

Malzahar

Always use W+E for shut down his passive and after go in. Rush Quicksivler slash vs his ultimate.

Yasuo

Sylas

Ahri

When you will ult her. Always safe your W. Start with R and follow her R with your W. The best time for your ultimate is when she waste her charm (E)

Orianna

Karthus

Azir

Until your 4lvl he will bully you. So farm jsut with Q. After you can start trade with him with your WEQ.

Brand

When he waste Q (stun) go in!

Kassadin

Always safe your W for follow him when he use Rift walk (R). Kassadin is danger for Zed just in late game.

Lux

Veigar

Vel'Koz

Ryze

Twisted Fate

The easiest matchup for Zed. Twisted Fate doesn't have escape (just R)
So try to bait him for pick yellow card and wait until he will throw it. When you see card is flying on you. Dodge it with Death Mark (R).